EP2881750A1 - Gradient system for magnetic resonance imaging - Google Patents

Abstract

A magnetic resonance imaging gradient system comprising three gradient coils (032) having current-carrying conductors (013) arranged on planar or curved surfaces (080, 030a), the current-carrying conductors of n being the three gradient coils, where n = 2 or n = 3, are closed in the azimuthal direction, semi-closed or open (013, 021) and each generate a magnetic gradient field, wherein the gradient directions are orthogonal to each other, characterized in that the planar or curved surfaces (080, 030a ) of the n gradient coils are formed spirally (036) and / or stepped (032), and that the current-carrying conductors of the n gradient coils are identically shaped (038a, 038b, 038c). Thus, the problems of the prior art can be handled elegantly, which are based primarily on the fact that the known gradient systems consist of coils, which may be substantially similar or even almost the same design, but have no consistently identical construction.

Description

The invention relates to a gradient system for magnetic resonance imaging comprising three gradient coils having current-carrying conductors arranged on planar or curved surfaces, wherein the current-carrying conductors of n of the three gradient coils, with n = 2 or n = 3, in the azimuthal direction are closed, half-closed or open formed and each generate a magnetic gradient field, wherein the gradient directions are orthogonal to each other.

Such a gradient system is known from EP 1 122 552 B1 (= Reference [P1]).

FIELD OF THE INVENTION

The present invention relates generally to the field of magnetic resonance imaging. In particular, it relates to a novel gradient system for a magnetic resonance imaging ("MR" Tomograph).

DISCUSSION OF THE PRIOR ART

In the early 1970s, Paul Lauterbur [1] and Peter Mansfield [2] independently recognized that spatial coding can be made possible by means of gradient fields. This discovery was followed by a variety of inventions, which were made possible by the fact that the magnetic resonance technology could now also be used as an imaging method.

The basic principle of gradient coding is well known, shown for example in reference [3]. If a magnetic field (gradient field) is superimposed on the z-direction-oriented constant main magnetic field whose z-component varies linearly in a certain spatial direction, the Larmor frequency of the affected spins also changes linearly in that direction, so that by analyzing the frequency spectrum of the recorded signal can be separated along this direction.

If only a single gradient field is used, location information can only be reconstructed along a single spatial direction. Therefore, three fields are required for the three-dimensional examination of objects, which vary locally along different spatial directions that do not lie in one plane. As a rule, three are global on each other generates orthogonally gradient fields that vary linearly along the x, y, and z directions, respectively.

The individual gradient fields are generated by gradient coils, which together form the gradient coil system (here also briefly: gradient system). In particular, open, cylindrical gradient systems will be used on the sides; for open tomographs there are biplanar gradient systems. Also described in the prior art are gradient systems with more complicated geometries that are better adapted to the shape of the objects to be measured, e.g. Reference [4].

The basic model for a cylindrical z-gradient coil (longitudinal coil) is a Maxwell coil consisting of two conductor loops of opposite polarity. The basic model for a cylindrical x and a y coil (transverse coil) differs significantly from that of the z coil and is formed by a coil consisting of four saddle-shaped subelements, shown for example in reference [P2].

The problem with such gradient systems in which the longitudinal coil and the transverse coils have different designs is in particular that the coils have different specifications and thus other limitations regarding their own properties (eg switching speed, achievable gradient strength) as well as their external influence (eg peripheral nerve stimulation). Eddy currents) has. This results in a high construction and specification effort, prevents flexible handling during the measurement and results in inaccuracies that can not optimally bring out the diagnostic value of MRI scans.

For this reason, a gradient system has been proposed in reference [P1], which reduces the differences between all three gradient coils. This is achieved by the fact that the three coils do not have gradients along the x, but along three oblique axes running in space, which merge into each other by a rotation of 120 ° about the z-axis. This can be achieved, for example, by generating gradients along the following (in this case orthogonal) axes: $${\mathbf{e}}_1^{\text{'}}=\frac{1}{\sqrt{6}}\left(\begin{array}{c}2\\ 0\\ \sqrt{2}\end{array}\right).{\mathbf{e}}_2^{\text{'}}=\frac{1}{\sqrt{6}}\left(\begin{array}{c}-1\\ \sqrt{3}\\ \sqrt{2}\end{array}\right).{\mathbf{e}}_3^{\text{'}}=\frac{1}{\sqrt{6}}\left(\begin{array}{c}-1\\ -\sqrt{3}\\ \sqrt{2}\end{array}\right)\mathrm{,}$$

gegenüber der Transversalebene ("magic angle") und sind jeweils gegenüber den anderen Achsen um 120° in die eine bzw. in die andere Richtung um die z-Achse rotiert. Anders als bei einem typischen Gradientensystem, bei dem nur eine Symmetrie bezüglich der x- und der y-Spule besteht, besteht bei einem solchen "Magic-Angle"-Gradientensystem eine Symmetrie bezüglich aller drei Spulen, so dass Spulen gebaut werden können, die sich sehr ähnlich sind, so dass die oben angesprochenen Probleme zumindest reduziert werden.These axes form a tilt angle of ${\tan }^{-1}\left(e_l/e_t\right)={\tan }^{-1}\left(1/\sqrt{2}\right)=$

relative to the transverse plane ("magic angle") and are rotated in each case with respect to the other axes by 120 ° in the one or the other direction about the z-axis. Unlike a typical gradient system, where there is only one symmetry with respect to the x and y coils, such a "magic angle" gradient system has symmetry with respect to all three coils, so that coils can be built that will are very similar, so that the above-mentioned problems are at least reduced.

However, the coils of cylindrical geometry described in [P1] are only substantially the same and not identical, so that the above-described problems with the invention disclosed in [P1] can only be partially remedied.

The background is that the conductors of a gradient coil of a cylindrical gradient system are typically located on a cylindrical surface of constant radius, see for example reference [P3]. A gradient system thus typically consists of three concentric layers of slightly different radii, each layer containing the current conductors of one of the three gradient coils, as in the case of the "Magic Angle" gradient system specifically described in [P1]. Due to slightly different radii thus exist furthermore differences with respect to the individual gradient coils, these are therefore only substantially the same and not identical.

The same applies to conventional gradient systems which generate gradients along the x, y and z axes. In these conventional gradient systems, not only do the transverse coils, i. x and y coil, compared to the longitudinal coil, i.e. z coil, different properties, but, due to the different radii, and the two transverse coils themselves. These are therefore only substantially the same and not identical.

The fact that the prior art coils can not be constructed identically entails another problem: currently, each of the three coils has to be designed differently for itself. This results in high research and development costs. In addition, the different nature of the coils results in a complex and therefore expensive production process, which also includes a series of manual operations.

In the following, by way of example, state of the art will be described, which in general has high relevance for the design of efficient gradient systems, and thus also for the present invention.

In the construction of gradient systems, as is known from reference [P2], attention is paid to a balanced (in terms of power) construction. In addition, in order to avoid eddy currents, gradient systems are typically equipped with compensation shields ("active shield"). This technology has been known for a long time, for example from reference [P4], see also References [10,11]. As a rule, three further concentric layers with significantly larger radii than the three inner gradient coils are used for this purpose. Efficiency gains can be achieved by using the side flanks of the cylindrical geometry, the three inner gradient coils are wired to the respective associated external compensation coils, as known from reference [P5], see, for example, reference [12]. Also, in addition to external field compensation, 3D designs may be beneficial where current conductors can be located in a whole volume, not just on given surfaces (see reference [9]).

Coil geometries are usually optimized for the purpose of generating highly efficient gradient fields, while at the same time requiring the highest possible degree of linearity, for example explicitly in reference [P6] or reference [P7]. Beneficial in this regard are the standard designs in which the conductors are closed along the azimuthal direction on the cylinder surface, i. are not interrupted. Reference [P8], however, describes an open design in which the cylindrical coils are separated into upper and lower halves to bring them closer to the object under examination. The invention described in reference [P8] deals with the problem caused by the azimuthal interruptions of the current conductors and notes that such an interruption is possible without significant efficiency losses.

In order to facilitate the discovery of coil designs according to the invention, systematic methods are briefly presented which help to develop efficient coil designs. A variety of methods are known in the art, which can be used to develop more efficient coil designs than the basic models described above.

An overview of the state of the art can be found in this regard in reference [P9]. There are both analytical and numerical methods. The method of reference [P10], well summarized in reference [P8] and the methods described in references [4] to [9] may be mentioned here by way of example. While initial methods (see references [5], [6]) In the case of newer methods (see references [4], [7], [8]), it is possible to specify arbitrary surfaces for current distributions, or even three-dimensional volumes (see reference [9]). As a rule, very good designs can be determined in disregard of temporal phenomena (Biot-Savart law, see References [4] to [7]), but there are also methods that co-model temporal phenomena (see reference [8]).

By way of example, the method presented in reference [7] is briefly presented here. In this method, a stream function is determined in a first step. In a second step, a practical fingerprint ladder design is derived based on this stream function .

To determine the stream function , the procedure is as follows: First, a coil geometry is specified, ie, a planar or curved surface is selected, on which later current-carrying conductors are to be arranged. This surface may be, for example, a cylinder open on the sides. The surface is then split into a large number of triangles using a meshing algorithm. For example, a Delaunay triangulation method would be possible. Thereupon, at each corner of each triangle, a basis function is determined which depends solely on the geometry of the mesh. Details can be found on page 70 and in Figures 3 to 5 of reference [7], a definition of the basis function is given by equation [[9]] in reference [7].

The current distribution on the surface is now given by a linear combination of the basis functions, whereby the associated weights are still to be determined. In a similar way, a stream function is defined as a linear combination of basic functions, the weights being the same as those of the current distribution. The stream function is defined so that the spatial gradient of the basis functions just the basic functions of the

Current distribution results. The exact relation is given by equation [[6]] in reference [7]. To determine the stream function , it is sufficient to determine the weights. The weights are determined by formulating and solving a suitable optimization problem. The formulation of the optimization problem is exhausted in the choice of a suitable target function, described by equation [[1]] in reference [7]. This includes a first term that punctures the deviation from a given magnetic field (typically a linear magnetic field in the x, y, or z direction), a second term that measures the magnetic energy (in reference [4] takes place on it a term that describes the power loss) and a third term that uses Lagrangian multipliers to provide the constraints that ensure that the current distribution found is well-balanced (see equation [[4]] in reference [7]) ,

Once this objective function is chosen, the optimization problem is to minimize it. For this, the objective function is derived from the weights to be determined and the Lagrange multipliers, and the result is set to zero. From this procedure results in a linear system of equations ZI = b, in which the matrix Z and the right side b depends only on the given coil geometry, the predetermined magnetic field and the other target function and the sought weights are given directly by components of the vector I. By inversion of the equation system, for example by means of Gaussian elimination or by determining the pseudo-inverses of Z , I can be determined. Thus, the weights of the stream function are determined and thus also the stream function itself on the given area.

In a second step, the position and form of current conductors, which should form the finished coil, can now be derived from the stream function . A possible procedure is described on page 73 in [7]. It is known that the contours of the stream function form the fingerprint design of coils. Give the contours Thus, a direct indication for the construction of a coil by - at the choice of a freely determinable number of contour lines - wires of constant current along the contours are placed, or by a large PCB at the location of the contour lines (or just between two such lines) conductive material is removed.

However, it is still important to ensure that the contour lines often form closed lines, so that at certain points the contour lines should be connected to each other, or by a wirbeiförmige lines is selected. The methods used for this purpose are well known, see, for. For example reference [P6], filed as early as 1983. An example of a fingerprint design of a transverse coil (z-coil) can be found in reference [P6], an example of a fingerprint design of a longitudinal coil can be found in reference [ P4].

SUMMARY OF THE INVENTION

The object of the present invention, in contrast, is to obviate the problems of the prior art described above, which are primarily based on the fact that the known gradient systems consist of coils which, although substantially similar or even almost the same design, are not consistent have identical construction .

This object is achieved in a surprisingly simple as well as effective manner in that a generic gradient system is provided with the features defined above, in which either all three or at least two of the three gradient coils are constructed geometrically exactly identical, which is achieved in that the coils are formed spirally and / or step-shaped.

PREFERRED EMBODIMENTS OF THE INVENTION

Of particular interest are, according to the invention, modified gradient systems for MR tomographs with a cylindrical bore opening, i. Gradient systems that are cylindrically shaped. The use of identical gradient coils requires that the coils are not arranged on concentric shells of different radii. However, it is possible, for example, a step-shaped or spiral structure in which the conductors also have a radial component. If a gradient system is used for a tomograph in which three gradient directions are generated, which merge into one another by means of a rotation of 120 °, then such a spiral construction-as will be described in detail later-leads to the desired success. A similar principle can also be used to construct a gradient system consisting of a longitudinal coil and two transverse coils of identical construction rotated by 90 ° with respect to each other.

Of interest, however, coil designs according to the invention for gradient systems, which are formed planar or biplanar whose gradient coils can be constructed identically constructed, but their fields are not identical, since they must be conventionally assembled on different levels to form a gradient. Again, as shown below with reference to a specific embodiment, a helical structure according to the present invention provides a remedy.

Due to the no longer exactly cylindrical (respectively planar) construction, but the stepped, spiral or similar bending of the gradient coils, those gradient designs that are open along the azimuthal direction are the simplest to realize. More efficient, however, are designs that completely or at least partially wire the open sides together, ie closed or at least semi-closed. Some embodiments will be detailed later.

In addition to the particular features of the invention just mentioned, which are then essential if a true identity of the coil geometries is to be achieved, it is a great advantage of the present invention that it can be relatively easily implemented and can be directly integrated into existing magnetic resonance devices.

Thus, when finding optimal coil designs according to the invention, the same principles apply, which also apply to existing coil designs. For example, care should generally be taken to ensure that the designs are balanced in terms of force or, for example, that an active shielding of the magnetic field to the outside using compensation coils is usually useful.

In order to find such optimal designs, basically the same methods known to the person skilled in the art can be used to find also conventional optimal coil designs. The prior art thus holds a number of possibilities ready to implement the invention effectively.

From the construction of the gradient system according to the invention, although some peculiarities arise, but the basic requirements are the same as in conventional gradient systems. As a result, with his knowledge of the state of the art and with the information given in this description, the person skilled in the art is not only enabled to find optimum coil designs according to the invention; Based on these designs, he will also know how suitable Gradient system can be constructed and he will be aware of how he can integrate and control it in an existing magnetic resonance device, since in this respect there are no significant peculiarities to conventional gradient systems.

By using identical gradient coils, a gradient system is made available, which on the one hand has particularly advantageous properties (for example with regard to eddy current compensation, electrical control, trajectory stability or heat generation), but on the other hand also offers advantages in terms of development and design and thus potential for cost savings. So it is enough to develop only an optimal design for multiple coils. In addition, a spiral-shaped construction makes it possible, for example, to place the individual printed circuit boards of the gradient coils next to one another and to wind them in a simple manner in a single production step around a prefabricated cylindrical mounting element.

• a. stromführende Leiter aufweisen, die auf planaren oder gekrümmten Flächen angeordnet sind, wobei die stromführenden Leiter von n der drei Gradientenspulen, mit n=2 oder n=3, in azimutaler Richtung geschlossen, halb-geschlossen oder offen ausgeformt sind und
• b. jeweils ein magnetisches Gradientenfeld erzeugen, wobei die Gradientenrichtungen orthogonal zueinander sind,

dadurch gekennzeichnet,
dass die planaren oder gekrümmten Flächen der n Gradientenspulen spiralförmig und/oder stufenförmig ausgeformt sind,
und dass die stromführenden Leiter der n Gradientenspulen identisch ausgeformt sind.In particular, within the scope of the present invention, there is a gradient system for magnetic resonance imaging, which comprises three gradient coils, which

• a. have current-carrying conductors which are arranged on planar or curved surfaces, wherein the current-carrying conductors of n of the three gradient coils, with n = 2 or n = 3, in the azimuthal direction closed, half-closed or open-shaped and
• b. each generate a magnetic gradient field, wherein the gradient directions are orthogonal to each other,

characterized,
that the planar or curved surfaces of the n gradient coils are formed spirally and / or step-shaped,
and that the current-carrying conductors of the n gradient coils are formed identically.

It should be noted that the arrangement on surfaces means that the conductors are geometrically arranged on surfaces. A planar surface may have a slight curvature by (imagining) bending a flat surface (see below). In that regard, linguistically, the reference surface is replaced by (imaginary) modification. Of particular importance are embodiments in which the gradient coils each generate a linear magnetic gradient field.

In a preferred embodiment, the gradient system is characterized in that the n identical gradient coils are converted into each other when the gradient system about a z-axis of the gradient system in the case of n = 2 by an angle α 1 = 90 ° or in the case of n = 3 irrespective of whether one or the other direction is rotated in an angle α 2 = 120 °, the gradient system thus has a 90 ° symmetry with respect to the n identical gradient coils in the case of n = 2 or, in the case of n = 3 has a 120 ° symmetry.

It should be noted that with identical gradient coils it is meant that the current-carrying conductors of these gradient coils are identical. The term "the n identical gradient coils" can thus be replaced by "the identically shaped current-carrying conductors of the n gradient coils" or by a similar formulation. It should also be noted that the 90 ° symmetry or 120 ° symmetry with respect to the axis of rotation (referred to herein as "a z-axis of the gradient system"). In other words, the current-carrying conductors of the n of the three gradient coils are formed identically, if in the case of n = 2 by an angle α 1 = 90 ° or in the case of n = 3 by an angle α 2 = 120 ° to a z -Axis of the gradient system are rotated, regardless of whether rotated in one direction or the other becomes. It should also be noted that "a z-axis" does not necessarily mean the z-axis of a Cartesian coordinate system, but rather a certain spatial direction. For a cylindrically shaped geometry, the z-axis corresponds to the cylinder axis, for a planar geometry the direction is orthogonal to the planar geometry (see below).

Also contemplated by the invention is a gradient system characterized by being cylindrically shaped and having the z-axis of the cylinder axis, i. the longitudinal axis of the cylindrically shaped gradient system corresponds.

In an advantageous embodiment, the cylindrically shaped gradient system is characterized in that n = 3 and α 2 = 120 °, and that the expansion of the n gradient coils in the azimuthal direction is 360 °, with azimuthal direction (the direction in Cartesian coordinates) direction on the cylinder-shaped surface around the cylinder geometry is meant.

In a further advantageous embodiment, the cylindrically shaped gradient system is characterized in that n = 3 and α 2 = 120 °, and that the expansion of the n gradient coils in the azimuthal direction is more than 360 ° α 2 = 120 °.

Of particular interest is also a cylindrically shaped gradient system, characterized in that n = 2 and α 1 = 90 °, and that the n = 2 identical gradient coils form transverse coils which generate orthogonal gradient fields in the transverse plane of the cylindrical geometry of the gradient system and the third gradient coil is formed as a longitudinal coil, and wherein the two transverse coils are formed open in the azimuthal direction.

Here, the open shape of the transverse coils means that the current-carrying conductors are formed open. Even a closed or semi-closed shape may be useful. The gradient fields are by definition linear gradient fields.

• c. offen,
• d. spiralförmig oder
• e. stufenförmig mit einer Stufe in der Mitte zwischen 0° und 180° ausgestaltet ist.

In a preferred embodiment, the cylindrically shaped gradient system with n = 2 identical transverse coils is characterized in that each transverse coil consists of two elements which each have an extension of 180 ° in the azimuthal direction and are rotated by 180 ° relative to each other, each element itself

• c. open,
• d. spiral or
• e. is designed stepwise with a step in the middle between 0 ° and 180 °.

The invention also extends to a gradient system which is characterized in that it is formed planar or biplanar, and that the z-axis corresponds to that axis, which is oriented orthogonal to the planar or biplanar conductor surfaces.

As already indicated above and explained in more detail below, in the context of this invention, a gradient system, which is constructed from essentially planar gradient coils, is referred to as planar (or biplanar). Even gradient coils, which emerge from an exactly flat coil by (imaginary) slight bending, are not referred to in this context as "essentially planar" but simply as "planar" (or biplanar). In the case of a substantially biplanar gradient coil, the z-axis is that which is determined by the shortest connection of the two partial coils. Is in the context of this invention of an azimuthal angle with respect to planar or Biplanar gradient systems spoken, so hereby the rotation angle with respect to this z-axis is meant.

An advantageous embodiment of a planar or biplanar gradient system is characterized in that n = 3 and α 2 = 120 °.

In a further advantageous embodiment, the planar or biplanar gradient system is characterized in that n = 2 and α 1 = 90 °, and that the n = 2 identical gradient coils form transverse coils, the orthogonal gradient fields in the transversal plane of the planar or bi-planar geometry of the gradient system generate, and the third gradient coil is formed as a longitudinal coil.

The advantageous embodiments mentioned above for a cylindrical shape of a gradient system each have a correspondence with a planar shape. These corresponding planar embodiments are also advantageous embodiments of this invention.

It should be noted that all advantageous embodiments of the gradient systems according to the invention can be configured such that the three main gradient coils are supplemented by compensation coils for active shielding of the magnetic fields to the outside.

In particular, it will be useful in a number of practical applications of the gradient systems of the invention if the gradient coils used are balanced in terms of their forces.

The present invention relates not only to gradient systems but also to gradient coils used in such a gradient system according to the invention.

In particular, the scope of the present invention also includes a gradient coil for use in a gradient system according to the invention of the type described above, the gradient coil having current-carrying conductors arranged on a planar or curved surface and closed, half-closed or open in the azimuthal direction and wherein the gradient coil is constructed of one or two elements and, if the gradient coil consists of one element, has an extension in the azimuthal direction of 360 ° or more or, if the gradient coil consists of two elements, each element has an extension in azimuthal Has direction of 180 °,
characterized,
that each element is formed spirally and / or stepped.

In the case where the gradient coil consists of two elements, it is advantageous if the step-shaped configuration of the elements has a step in the middle between 0 ° and 180 °. Of particular interest are (substantially) cylindrical or (substantially) planar shaped gradient coils. It should also be noted that constructive peculiarities exist from the fact that the gradient coil is to be used in a gradient system according to the invention. Thus, the elements must be formed in a spiral and / or step shape such that n = (2-1) or n = (3-1) further identical gradient coils can be arranged to form a gradient system. This means in particular that a "nested nesting" must be possible. In other words, a gradient coil according to the invention is characterized in that, in the case of an imaginary (n-1) -fold identical replica of the coil, with n = 2 or n = 3, the surfaces on which the current-carrying conductors of the n coils are arranged are not penetrate. It should be noted that the surfaces of current-carrying conductors are not merely imaginary surfaces without expansion, but that these surfaces a have real thickness, which depends on the thickness of the current-carrying conductors used and their insulation. This range is usually no less than one millimeter and no more than one or a few inches, depending on the size and performance of the coil. The person skilled in the art is aware of what thickness should be realized in practice.

Of the above-mentioned embodiments, gradient coils in which no penetration of the surfaces takes place are of interest, if the gradient coil and the n imaginary identically reproduced gradient coils form a gradient system in the sense of this invention. This means, for example, that the gradient coil is characterized in that no penetration of the surfaces takes place with a gradient system which is formed from the gradient coil and the imaginary identically reproduced gradient coils, which is characterized in that the n identical gradient coils are converted into one another, if the Gradient system is rotated about a z-axis of the gradient system in the case of n = 2 by an angle α 1 = 90 ° or in the case of n = 3 by an angle α 2 = 120 °, regardless of whether in one or the other Direction is rotated, the gradient system thus with respect to the n identical gradient coils in the case of n = 2 has a 90 ° symmetry or in the case of n = 3 has a 120 ° symmetry. With regard to a gradient coil in the context of this invention, the same applies to the other embodiments of a gradient system according to the invention described above.

Further advantages of the invention will become apparent from the detailed description and the drawings. Likewise, according to the invention, the above-mentioned features and those which are still further developed can each be used individually for themselves or for a plurality of combinations of any kind. The embodiments shown and described are not to be understood as exhaustive enumeration, but rather have exemplary character for the description of the invention.

BRIEF DESCRIPTION OF THE DRAWING

The figures of the drawing explained briefly below serve to illustrate exemplary embodiments of the invention. In addition, they are intended to illustrate how the invention may be carried out and in part to illustrate problems for which solutions are provided in the detailed description.

• Fig. 1 stellt ein optimiertes Fingerprint-Design sowie eine passende mögliche Anordnung von Stromleitern für eine zylinderförmige Gradientenspule mit offenen seitlichen Enden, aber geschlossenen Leiterplatten entlang der azimutalen Richtung dar; die Spule erzeugt einen Feldgradienten mit Transversal- wie auch mit Longitudinalkomponente.
• Fig. 2 stellt ein optimiertes Fingerprint-Design für eine erfindungsgemäße spiralförmige Spule dar mit offenen seitlichen Enden und nicht-geschlossenen (i.e. offenen) Leiterplatten entlang der azimutalen Richtung.
• Fig. 3 zeigt einen bekannten schalenförmigen Aufbau eines Gradientensystems mit Kompensationsspulen in Seitenansicht sowie zwei verschiedene mögliche Anordnungen eines erfindungsgemäßen Gradientensystems.
• Fig. 4 zeigt ein offenes spiralförmiges Design, welches nicht wie die Designs der Fig. 1 und Fig. 2 kräftemäßig ausbalanciert ist und gibt Aufschluss darüber, welche Geometrie die Kompensationsströme für dieses Design haben müssen, um effektiv die gleiche kräftemäßig ausbalancierte Gesamtgeometrie aufzuweisen wie das in Fig. 1 dargestellte Design.
• Fig. 5 zeigt beispielhaft eine Leiterschleife für drei verschiedene Konstruktionen und veranschaulicht, dass es möglich ist, auf einfache Weise kräftemäßig ausbalancierte offene Spulendesigns zu entwickeln, wenn die Spule einen Winkel von etwas mehr als 360° entlang der azimutalen Richtung einschließt.
• Fig. 6 illustriert das Problem, dass bei geschlossenen erfindungsgemäßen Designs verbindende Stromleiter einer Gradientenspule die Leiterplatten der zwei anderen Gradientenspulen passieren müssen. Die Abbildung dient der Veranschaulichung für Lösungen, die im Text ausführlich beschrieben sind.
• Fig. 7 illustriert ein Fingerprint-Design einer herkömmlichen Transversalspule sowie zwei erfindungsgemäße Varianten eines Gradientensystems, bei dem die x- und die y-Spule völlig identisch ausgestaltet sind.
• Fig. 8 illustriert die Oberfläche einer Gradientenspule für ein erfindungsgemäßes planares Gradientensystem, bzw. die Oberfläche des oberen oder unteren Teils einer Gradientenspule für ein biplanares Gradientensystem.

The invention is illustrated in the drawing and will be explained in more detail with reference to embodiments.

• Fig. 1 Figure 3 illustrates an optimized fingerprint design as well as an appropriate possible array of current conductors for a cylindrical gradient coil with open side ends but closed circuit boards along the azimuthal direction; the coil generates a field gradient with transverse as well as with longitudinal component.
• Fig. 2 Figure 3 illustrates an optimized fingerprint design for a spiral coil according to the invention with open lateral ends and non-closed (ie open) circuit boards along the azimuthal direction.
• Fig. 3 shows a known shell-shaped structure of a gradient system with compensation coils in side view and two different possible arrangements of a gradient according to the invention.
• Fig. 4 shows an open spiral design, which is not like the designs of the Fig. 1 and Fig. 2 balanced in terms of force and provides information about which geometry the compensation currents have to have for this design in order to effectively have the same balanced overall geometry as that in Fig. 1 illustrated design.
• Fig. 5 FIG. 12 exemplifies a conductor loop for three different constructions and illustrates that it is possible to easily develop force balanced unbroken coil designs when the coil includes an angle of slightly more than 360 ° along the azimuthal direction.
• Fig. 6 illustrates the problem that with closed designs according to the invention connecting conductors of a gradient coil must pass through the circuit boards of the two other gradient coils. The figure is an illustration of solutions that are described in detail in the text.
• Fig. 7 illustrates a fingerprint design of a conventional transverse coil and two variants of a gradient system according to the invention, in which the x and y coil are configured completely identical.
• Fig. 8 illustrates the surface of a gradient coil for a planar gradient system according to the invention, or the surface of the upper or lower part of a gradient coil for a biplanar gradient system.

DETAILED DESCRIPTION OF THE INVENTION

In the following, principles relevant to the invention as well as specific embodiments of the invention will be described in detail, reference being partially made to the drawings. However, the invention should not be limited to these specific embodiments.

Fig. 1 provides an optimized fingerprint design ( Fig. 1a , 001) and a suitable possible arrangement of conductors ( Fig. 1b , 013) for a cylindrical gradient system with open lateral ends but closed circuit boards along the azimuthal direction 002; the Dashed lines 003, 011 indicate that it is a closed geometry, so that contour lines and current conductors, which emerge on one side of the image, reappear on the other side. This in Fig. 1 Design presented is an optimized result, which is as in one Fig. 3a shown gradient system with a bowl-shaped structure (without compensation coils) heard. The English terms "angle", "length", "radius" and "power supply" in the drawings mean "angle", "length", "radius" and "power source".

Even if the in Fig. 3a This example is nevertheless interesting for the present invention, since this or at least a similar design for the closed, inventive, in Fig. 3b illustrated design can be used, s. in more detail below in the section before the detailed description of Fig. 2 , The design 001 generates a field gradient with transverse as well as with longitudinal component with a tilt angle of 45 ° to the transverse plane along a direction, which is denoted here by e. For example, an angle of 35.26 ° (magic angle) is possible; this, as will be shown later, is even useful for the present invention, as such an angle results in an orthogonal coding system and requires fewer turns around the cylindrical geometry (see below the second section of the detailed description) Fig. 6 ).

This in Fig. 1 Design shown is on a closed cylinder with a radius of 35cm. Rotation of ± 120 ° and optimization for two slightly different radii would result in non-identical but similar designs that could be used for a gradient system, as in [P1] = EP 1 122 552 B1 is described. It is striking that the design has both elements of a longitudinal coil (parallel windings around the bobbin) and elements of a transverse coil (four vortex-shaped coil elements), which is due to the fact that the coding axis both a transversal and has a longitudinal component. The surface of the design has an extension in the z-direction of -60 cm to 60 cm, the current distribution thus extends over a distance of 120 cm in the z-direction.

z = [-60 cm, 60 cm]}, wobei x(θ, z) = r ₀ cos θ, y(θ, z) = r ₀ sin θ und z(θ, z) = z, wobei r ₀ = 35cm gewählt wurde.This in Fig. 1 The design shown was calculated by following essentially the method described in [7], although elements from [4] and [8] were also used. First, the cylindrical curved surface of the coil, on which the current-carrying conductors are arranged, was parameterized by the z-coordinate and the azimuthal angle θ , ie the surface for the design 001 was represented by $S=\{\mathbf{x}\left(\theta ,z\right)\in {\mathbb{<figure-callout\; id="3"\; label="R"\; filenames="imgf0006.png"\; state="\{\{state\}\}">R</figure-callout>}}^3|\theta =\left[0°.360°\right].$

z = [-60 cm, 60 cm]}, where x ( θ, z ) = r ₀ cos θ , y ( θ, z ) = r ₀ sin θ and z ( θ, z ) = z, where r ₀ = 35cm was chosen.

Then this area was triangulated in parameterized space. For this purpose, the θ - z plane was first divided into regular quadrilaterals, which were then divided once again so that two triangles were generated from each quadrilateral. In total, 2880 triangles were generated. Because of the closedness of the design (ie the closedness of the current-carrying conductors), it was ensured that triangles in the azimuthal direction have no boundary, but are also in contact with each other at 0 °.

Next, a stream function Ψ = Σ _i I _i φ _{i was} generated with weights I _i and basis functions φ _i , but not the basic functions shown in [7] were selected, but so-called "triangular linear shape functions" known to those skilled in the art. , Let j be defined as the current density. Now, j = ∇ × ( Ψ n ), where n is the normal vector to the surface; Because of this relationship, the current density was calculated using the definition of the stream function .

gewählt. Dabei bedeutet B_Z die Magnetfeldstärke, die mit Hilfe des Biot-Savart-Gesetzes auf Grundlage von j berechnet werden kann. $B_z^t$

stellt das zu approximierende Magnetfeld dar, welches durch B(x) = Gx = Gex gegeben ist, wobei G die Stärke des Magnetfeldgradienten (=Gradientenstärke) bezeichnet.Next became the target functional $\mathrm{\Phi }=\underset{k=1}{\overset{K}{\Sigma }}{\left[B_z\left({\mathbf{x}}_k\right)-B_z^t\left({\mathbf{x}}_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0006.png"\; state="\{\{state\}\}">k</figure-callout>}}\right)\right]}^2+\mathit{\alpha P}+\mathbf{.lambda..sub.m}$

selected. Where _{Bz is} the magnetic field strength that can be calculated using the Biot-Savart law based on j . $B_z^t$

represents the magnetic field to be approximated given by B (x) = Gx = Gex, where G denotes the strength of the magnetic field gradient (= gradient strength).

The deviation from the wanted and the actual magnetic field is determined in an ROI (region of interest) by choosing K equidistant points x _k , which are all within the ROI and fill it. For the calculations, a spherical ROI with a radius of r _ROI = 20cm was chosen and K = 1000. P describes the power loss given by equation [[2]] in [4] and is directly related to surface geometry and current distribution.

α is a parameter that represents a trade-off between field linearity and minimization of power dissipation. This parameter was chosen such that the largest deviation from linearity was 5% ± 0.01%. The deviation was determined by relating the maximum difference between desired and actual magnetic field strength within the ROI to the maximum desired magnetic field strength within the ROI by dividing the two values.

The vectorial magnitude λ describes Lagrange multipliers and M the three components of the torque as defined in equations [[19-21]] of [7]. With the addition of this third term was thus ensured that the resulting gradient coil is balanced in terms of strength.

The further procedure did not differ from the method described in [7] and repeated in the description of the state of the art. The solution of the resulting system of equations was the "\" operator used by Matlab (The MathWorks, Natick, MA). It should be noted, however, that this invention is not limited to gradient coils that can be found by the method used herein. Any method can be used, all that matters is that the resulting fields produce a gradient along the direction e. Even a purely intuitive approach can lead to meaningful arrangements of current conductors of a gradient coil (for example, the current conductors connecting the upper conductors to the lower conductors have been used) Fig. 4 and Fig. 5 not with the help of this numerical method, but due to other considerations).

Widerstand 26 mΩ bei 26 den Konturlinien der stream function folgenden Leitern mit einer Leiterdicke von 3mm und der Leitfähigkeit von Kupfer (6 · 10⁷ m^-1Ω^-1).This in Fig. 1 The force-balanced design shown has the following properties: Gradient of Design 001: $86\frac{\mu \mathrm{T}}{\mathrm{m}\cdot \mathrm{A}}\mathrm{,}$

Resistance 26 m Ω at 26 conductors following the contour lines of the stream function with a conductor thickness of 3 mm and the conductivity of copper (6 · 10 ⁷ m ^-1 Ω ^-1 ).

• Gradientenstärke der Longitudinalspule/Transversalspule: $135/67\frac{\mu \mathrm{T}}{\mathrm{m}\cdot \mathrm{A}};$
  
  Widerstand: 40/21 mΩ.

The method discussed in the last section was also used to find current distributions for a transverse and a longitudinal coil with a radius of 35cm (the current distribution of the transverse coil is in Fig. 7a shown). These had the following characteristics:

• Gradient strength of the longitudinal coil / transverse coil: $135/67\frac{\mu \mathrm{T}}{\mathrm{m}\cdot \mathrm{A}};$
  
  Resistance: 40/21 m Ω.

The comparison of the values shows that the coil with an oblique coding direction has properties which lie between those which have conventional transverse and longitudinal coils, owing to the fact that the coding direction has a portion along the longitudinal axis and one in the transverse plane lies. So that's in Fig. 1 shown design more efficient than the design of a conventional transverse coil, but less efficient than that of a typical longitudinal coil.

Fig. 1b shows one too Fig. 1a suitable practical arrangement of current conductors which form a curved cylindrical surface with boundary 010. The dashed line 011 is intended to indicate that it is a closed geometry, so that current conductors, which emerge on one side of the image, on the other side again Pop up; the current-carrying conductor 013 are thus formed closed. A current supply conductor 012a of the current-carrying conductor 013 is connected to the cylinder surface with a power source 014 (the current source is reversed, of course, changes the flow direction and from the power supplying conductor is a stroma b carrying conductor and vice versa).

The current first flows to the first vortex, which conveys the current in smaller and smaller windings to the left. In the middle, the current leaves the vortex via a straight 015a (and thus without an effective contribution to the gradient field) straight along the negative z-axis and flows into the second vortex, which turns outward and is dextrorotatory. After a few vortex-shaped turns, the current leaves the vortex in the negative azimuthal direction and winds several times around the cylinder geometry. The subsequent conductor arrangement with vortices, conductor bridge 015b, vortices and windings corresponds to the arrangement just described, but rotated by θ - z coordinates by 180 °. The current exits the cylinder geometry in the vicinity of the current-carrying conductor 012a via a current-carrying conductor 012b, which provides a closed circuit via the current source 014 .

In the Fig. 1b drawn conductor arrangement was based on the in Fig. 1a shown contour lines of the stream function created. Although it would be possible to arrange current conductors so that they follow the contour lines immediately, however, such an arrangement provides difficulties in supplying the conductors with power. Therefore, it is common to make connections between the contour lines manufacture. For example, this can be done abruptly with the aid of short conductor bridges (see, for example, reference [P4]), or continuously (see, for example, reference [P6]). Fig. 1b shows an arrangement of the second category, so that a vortex-shaped design results (in the arrangement shown, the conductors have an average distance of two in Fig. 1a shown contour lines).

This in Fig. 1b Of course, the arrangement shown is just one of many possible examples of how to derive a useful array of conductors from a stream function design. Various methods are known to the person skilled in the art, for example the two approaches just mentioned (see eg [P10] = US 5,309,107 A . Fig. 7 . 8th ). Also, one skilled in the art will have sufficient knowledge of how, based on a found distribution of current carrying conductors, he would design the complete gradient coil and how he would drive it. For example, one skilled in the art will know which cross section the conductors should optimally have or how the conductors should be fixed, cooled and insulated. The person skilled in the art also knows methods that enable him to do so, for example, in the Fig. 1b shown ladder bridges 015a, b to be able to do by constructing the coil two layers, see for example in [13]. He will also design the geometry of the incoming and outgoing conductors according to the requirements that face him. In the Fig. 1b represented conductors 012a, 012b represent only one possible embodiment.

Although current distributions or arrangements of current-carrying conductors according to the invention differ in their specific geometry (ie in the surface on which the current conductors are arranged) of previously existing designs. This in Fig. 2 shown and in the section of the detailed description Fig. 2 discussed example as well as the one below in the section before the detailed description of Fig. 2 Employed considerations for the use according to the invention of the in Fig. 1 However, the design shown here shows that the differences are not so great that non-traditional methods are used could be used to construct a gradient coil and a complete gradient system from a stream function or an arrangement of current-carrying conductors and to insert this into an existing MR tomograph.

The person skilled in the art will therefore generally be able to resort to previously known methods within the scope of this invention. In particular, the apply to Fig. 1 explained details substantially for inventive gradient coils. For this reason, the representation of the limited in Fig. 2 illustrated inventive arrangement on the calculation of the stream function and the representation of the same by means of contour lines. Incidentally, apart from a few exceptions, the numerical calculation of optimal arrangements is dispensed with and the person skilled in the art is left to carry out the optimization himself, for which purpose the state of the art and the description of this invention provide sufficient information. However, reference is made in the following to particular features of arrangements according to the invention, which the person skilled in the art should take into account when designing gradient coils and gradient systems according to the invention.

bzw. $82\frac{\mu \mathrm{T}}{\mathrm{m}\cdot \mathrm{A}}$

aufwiesen. Trotz der Ähnlichkeit der resultierenden Anordnungen ergeben sich aufgrund des schalenförmigen Aufbaus mit unterschiedlichen Radien somit noch Effizienzunterschiede in Höhe von fast 10%, was beispielsweise Probleme in Bezug auf die Wärmeentwicklung während des Betriebes nach sich führen kann. Diese Unterschiede der Spuleneigenschaften und die damit zusammenhängenden Probleme werden behoben, wenn ein Gradientensystem in der Art konstruiert wird, wie in dieser Schrift beschrieben, wenn beispielsweise ein geschlossenes, stufenförmiges Design wie in Fig. 3b dargestellt verwendet wird mit drei identisch ausgestalteten Gradientenspulen, die aus geschlossenen stromführenden Leitern bestehen, die auf einer stufenförmigen Fläche angeordnet sind.As already mentioned, that can be done in Fig. 1 design used directly in a known from the prior art gradient system, which consists of concentric shells (see also Fig. 3a ). The problem is, however, that the two other gradient coils can not be constructed identically, but must have a different radius. So also designs were analogous to Fig. 1 calculated, however, with a radius of 34cm or 36cm instead of 35cm, which has an efficiency of $89\frac{\mu \mathrm{T}}{\mathrm{m}\cdot \mathrm{A}}$

respectively. $82\frac{\mu \mathrm{T}}{\mathrm{m}\cdot \mathrm{A}}$

exhibited. Despite the similarity of the resulting arrangements, the shell-shaped structure with different radii thus still results in efficiency differences of almost 10%, which for example causes problems with regard to heat generation can result during operation. These differences in coil properties and the problems associated therewith are overcome when constructing a gradient system of the type described in this document, for example when using a closed, stepped design as in FIG Fig. 3b is shown used with three identically designed gradient coils, which consist of closed current-carrying conductors, which are arranged on a stepped surface.

By way of example, an advantage is to be described, which arises because completely identical coils are used according to this invention. In the last section, it was shown that there are efficiency differences of up to 10% when gradient coils of a gradient system are constructed on layers of different radii, which in [P1] = EP 1 122 552 B1 according to the invention so that the gradient system does not have a 120 ° symmetry (ie, so that the arrangement does not have 120 ° symmetry with respect to the three gradient coils), although the coding directions themselves have this symmetry property. The same applies to the two transverse coils in a typically used xyz gradient system.

As a result, depending on the coding direction, the gradient system according to the prior art is differently efficient, so that the power loss also depends on the coding direction, which has the unfavorable effect that the heat generation also depends on the coding direction.

This in turn leads to limitations when taking pictures with an MR tomograph. It will now be shown in detail that the power loss is independent of the coding direction when a gradient system according to the invention is selected.

This is shown by means of a magic-angle gradient system, but the same considerations apply to transversal coils formed according to the invention, it being also noted here that a constant power dissipation exists only for those coding directions which have the same z-component, i. the considerations apply only to variations of the coding direction along a vector in the transverse plane.

orthogonal aufeinander stehen. Aufgrund der Tatsache, dass alle drei erfindungsgemäßen Gradientenspulen die gleiche Bauweise aufweisen, haben sie die gleiche Effizienz g und erzeugen somit bei gleicher Stromstärke I dieselbe Gradientenstärke G = gI. Die vektorielle Größe der Gradientenstärken ist somit gegeben durch ${\mathbf{G}}_{1,2,3}=\mathit{gI}{\mathbf{e}}_{1,2,3}^{ʹ}\mathrm{.}$

Furthermore, it is assumed that the three gradient directions generated by the gradient coils ${\mathbf{e}}_1^{\text{'}}.{\mathbf{e}}_2^{\text{'}}\mathrm{and}{\mathbf{e}}_3^{\text{'}}$

orthogonal to each other. Due to the fact that all three gradient coils according to the invention have the same construction, they have the same efficiency g and thus generate the same gradient strength G = gI for the same current intensity I. The vectorial magnitude of the gradient strengths is thus given by ${\mathbf{<figure-callout\; id="1"\; label="G"\; filenames="imgf0006.png"\; state="\{\{state\}\}">G</figure-callout>}}_{1.2.3}=\mathit{gI}{\mathbf{<figure-callout\; id="1"\; label="e"\; filenames="imgf0006.png"\; state="\{\{state\}\}">e</figure-callout>}}_{1.2.3}^{\text{'}}\mathrm{,}$

wobei es aufgrund der linearen Unabhängigkeit von ${\mathbf{e}}_1^{ʹ},{\mathbf{e}}_2^{ʹ}\mathrm{und}{\mathbf{e}}_3^{ʹ}$

genau eine Kombination von Stromstärken I _1,2,3 gibt, die dieses Gradientenfeld erzeugt. Soll nun unabhängig von der Kodierrichtung er ein Gradientenfeld derselben Stärke G ₀ erzeugt werden, so gilt: $\mathit{const}=G_0^2={\Vert {\mathbf{G}}_r\Vert }^2={\Vert g\sum _{i=1}^3{I}_i{\mathbf{e}}_i^{ʹ}\Vert }^2=g^2\sum _{i=1}^3{I}_i^2$

und somit auch $\sum _{i=1}^3{I}_i^2=\mathit{const}\mathrm{.}$

Dies ist eine unmittelbare Folgerung aus der Orthogonalität von ${\mathbf{e}}_1^{ʹ},{\mathbf{e}}_2^{ʹ}\mathrm{und}{\mathbf{e}}_3^{ʹ}$

Die Summe der Stromquadrate ist somit für alle Kodierrichtungen gleich.Now, in general, the coils can be operated with different currents I _1,2,3 . Due to the superposition principle, the result is the resulting gradient field ${\mathbf{G}}_r=\underset{i=1}{\overset{3}{\Sigma }}{\mathbf{G}}_i=G\underset{i=1}{\overset{3}{\Sigma }}{I}_i{\mathbf{e}}_i^{\text{'}}.$

it being due to the linear independence of ${\mathbf{e}}_1^{\text{'}}.{\mathbf{e}}_2^{\text{'}}\mathrm{and}{\mathbf{e}}_3^{\text{'}}$

exactly gives a combination of currents I _1,2,3 , which generates this gradient field. If now a gradient field of the same strength G ₀ is to be generated independently of the coding direction, the following applies: $\mathit{const}={\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">G</figure-callout>}}_0^2={\Vert {\mathbf{G}}_r\Vert }^2={\Vert G\underset{i=1}{\overset{3}{\Sigma }}{I}_i{\mathbf{e}}_i^{\text{'}}\Vert }^2={\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="imgf0006.png"\; state="\{\{state\}\}">G</figure-callout>}}^2\underset{i=1}{\overset{3}{\Sigma }}{I}_i^2$

and therefore too $\underset{i=1}{\overset{3}{\Sigma }}{I}_i^2=\mathit{const}\mathrm{,}$

This is an immediate consequence of the orthogonality of ${\mathbf{e}}_1^{\text{'}}.{\mathbf{e}}_2^{\text{'}}\mathrm{and}{\mathbf{e}}_3^{\text{'}}$

The sum of the current squares is thus the same for all coding directions.

wobei mit dem für alle drei Spulen gleichen Widerstand R für die Verlustleistung der einzelnen Spulen gilt: $P_{1,2,3}=R{I}_{1,2,3}^2\mathrm{.}$

Die gesamte Verlustleistung ist somit gegeben durch $P=\sum _{i=1}^3{P}_i=R\cdot \sum _{i=1}^3{I}_i^2=\mathit{const}\mathrm{.}$

Dieser Term ist wie oben gezeigt unabhängig von der Kodierrichtung. Damit ist bewiesen, dass die Behauptung wahr ist, bei identischer Bauweise der drei Spulen sei die Verlustleistung unabhängig von der Kodierrichtung, ein Vorteil, der nach dem Stand der Technik nicht besteht.Now, however, the power loss P is given by the sum of the resulting in each coil power dissipation P _1,2,3 , ie $P=\underset{i=1}{\overset{3}{\Sigma }}{I}_i.$

with the same resistance R for all three coils for the power loss of the individual coils: ${\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="imgf0006.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1.2.3}=R{I}_{1.2.3}^2\mathrm{,}$

The total power loss is thus given by $P=\underset{i=1}{\overset{3}{\Sigma }}{P}_i=R\cdot \underset{i=1}{\overset{3}{\Sigma }}{I}_i^2=\mathit{const}\mathrm{,}$

This term is as above shown independent of the coding direction. This proves that the claim is true that with identical design of the three coils, the power loss is independent of the coding direction, an advantage that does not exist in the prior art.

If now a gradient system with closed stepped surfaces of current-carrying conductors in the context of this invention as in Fig. 3b shown used and not a gradient system with cylindrical conductor shells, then an optimal distribution of conductors in this case is not very strong from the in Fig. 1b shown arrangement, since the short radial connecting conductors between the layers do not have a very large influence, since the radius changes only a few millimeters to a few centimeters.

So it would be possible, for example, in Fig. 1b To use immediately shown arrangement of conductors and shaping by suitable bending in the intended geometry. However, a gradient system with improved properties could be developed if the changed geometry were integrated directly into the calculation method used for the optimization. This will be shown in detail in the next section for a spiral open design, however, it will be appreciated by those skilled in the art how to apply the known optimization techniques to other cases, as well as to the just described case of a closed design with a stepped construction.

Fig. 2 shows a spiral design according to the invention 020, in which, first, the in Fig. 1 shown cylindrical surface of current-carrying conductors is not closed, but open, and secondly, the open sides not flush with each other, but radially offset by 3cm. The inner radius is r _i = 34cm, the outer r _α = 37cm. Note that in the context of this invention, basically the same property is meant when the terms "closed", "half-closed" or "open" refer to the whole

Gradient system, the gradient coils, the surfaces of current-carrying conductors or on the arrangement of the current-carrying conductor. The same applies if the term "design" is used or "the arrangement" or the like. The same applies to the terms "spiral-shaped and / or stepped", which describe a uniform property, regardless of whether it is spoken, for example, that the gradient coils (or elements of these coils) themselves have this property or the surfaces (or surfaces), on which the current-carrying conductors of the gradient coils are arranged.

The open design implies that the current carrying conductors 021 of the coil are openly formed in the azimuthal direction. The spiral design may also be referred to as "substantially cylindrical" or simply "cylindrical" in that the deviation from a pure cylindrical geometry is small and still well accommodated by a cylindrical bore. A gradient system, which consists of such spiral (and / or step-shaped) gradient coils, should therefore also be referred to as "cylindrical" itself. Insofar as there is no likelihood of confusion due to the context, this linguistic simplification also applies to the gradient coils themselves or to the surfaces on which the current-carrying conductors are arranged.

Fig. 2a shows optimized contour lines for the in Fig. 2b shown in side view spiral arrangement. Regarding the open design, note the following: While in Fig. 1 the page boundary 011 is drawn by dashed lines, it is in Fig. 2a consistently drawn (022), which makes it clear that the pages are not interconnected. Depending on the angle at which the surface is separated, is obtained by the used numerical method is a non-symmetrical arrangement or one which a 180 ° symmetry in the θ - having z plane. In this one In the example shown, an angle of 90 ° was chosen for the coding direction e in order to obtain the in 2a to produce shown almost symmetrical arrangement.

In the optimization problem, unlike the closed design, the triangles of the mesh of the right edge were not connected to those of the left edge. The sidelines 022 rather formed part of the edge in the calculation of an optimal design.

z = [-60 cm, 60 cm]}, wobei x(θ, z) = r(θ) cos θ, y(θ, z) = r(θ) sin θ und z(θ, z) = z, mit $r\left(\theta \right)=r_i+\left(r_a-r_i\right)\frac{\theta }{360°}\mathrm{.}$

Concerning the spiral shape, the following was considered in the calculation: Rather than in the second section of the detailed description Fig. 1 the following parameterization of the interface was used: $S=\{\mathbf{x}\left(\mathrm{\theta },\mathrm{z}\right)\in {\mathbb{<figure-callout\; id="3"\; label="R"\; filenames="imgf0006.png"\; state="\{\{state\}\}">R</figure-callout>}}^3|\theta =\left[0°.360°\right].$

z = [-60 cm, 60 cm]}, where x ( θ , z ) = r ( θ ) cos θ , y ( θ, z ) = r ( θ ) sin θ and z ( θ, z ) = z, With $r\left(\theta \right)=r_i+\left(r_a-r_i\right)\frac{\theta }{360°}\mathrm{,}$

bei einem Widerstand von 27 mΩ. Bezüglich der Gradientenstärke ergeben sich insofern im Vergleich zu einem geschlossenen Design lediglich Effizienzverluste von etwa 15%.In addition to these deviations, the same parameters were used as in the Fig. 1 a shown design. This in Fig. 2 shown design has a gradient strength of $73\frac{\mu \mathrm{T}}{\mathrm{m}\cdot \mathrm{A}}$

at a resistance of 27 m Ω. Regarding the gradient strength, this results in only about 15% efficiency losses compared to a closed design.

Fig. 3 shows in side view three different arrangements of the three gradient coils (with compensation coils), which form different gradient systems.

Fig. 3a shows a cup-shaped construction known from the prior art in which the conductors of the three gradient coils 030 have a slightly different but constant radius, thus forming closed superimposed cylinders so that the current-carrying conductors are geometrically curved on curved cylindrical surfaces 030a are located. Fig. 3a shows a situation in which the three gradient coils by three Compensation coils 031 are supplemented for active shielding of the magnetic fields to the outside. The three compensation coils are also arranged cup-shaped, the order of the compensation coils in relation to the gradient coils can basically be chosen arbitrarily, but typically have the same sequences, ie with increasing radius gradient coil 1, gradient coil 2, gradient coil 3, compensation coil 1, Compensation coil 2, compensation coil 3.

Fig. 3b also shows a closed design of a gradient system with three stepped gradient coils 032 and three compensation coils 033, but the three gradient and compensation coils and the (substantially) cylindrically shaped gradient system are constructed according to the invention since the coils have identical geometry, only rotated by 120 ° °. This means that if the gradient system is thus rotated about a z-axis of the gradient system (the cylinder axis) by an angle α 2 = 120 °, regardless of whether rotating in one direction or the other, the three identical coils (in geometrically). The gradient system thus has a 120 ° symmetry (with respect to the identical coils). This symmetry in identity of the three coils is achieved in that the current conductors of a coil do not have a constant total radius, but change the radius twice. Thus, in each case the first 120 ° or, as illustrated, nearly 120 ° on the first shell, the second 120 ° on the second shell and the third 120 ° on the third shell. At the junctions there are short conductor bridges 034a, 034b which have a radial current component. Conceivable is an open or semi-closed design, but is shown a closed design in which the third shell is completely connected to the first shell via short conductor bridges 035 .

Fig. 3c shows a spiral open design with three gradient coils 036 and three compensation coils 037 Fig. 3c contains illustrated arrangement each three identical gradient coils 038a, 038b and 038c, each rotated by 120 °. The same applies to the three compensation coils. In the Fig. 3c embodiment shown consists of coils which have a greater extent than 360 ° in the azimuthal direction and are open, in which the two ends 039a and 039b of the coil geometry thus enclose an angle of more than 360 °. Another embodiment, not shown, for example, encloses only a total angle of 360 °; For example, for this embodiment, gradient coils could be used with a design as in FIG Fig. 2 shown.

Other embodiments not shown are half-closed or completely closed. It is similar to the in Fig. 3b to ensure that the wiring is well-designed, s. also the discussion too Fig. 6 , In addition to many other possible embodiments, such is explicitly mentioned, in which the distance between the current-carrying conductors of the compensation coils to the center of the geometry is not as in Fig. 3b and Fig. 3c increases counterclockwise successively, but in a clockwise direction, ie opposite to the direction of the radial increase of the ladder of the main gradient coils.

The step-shaped design has, among other things, the advantage over the spiral design that it adapts in a very simple way to a cylindrical geometry, which can bring advantages in production; For example, simply shaped cylindrical mounting elements can be used without special design. However, there is an increased installation effort at the points where the conductors change from the inner to the outer layer.

This problem does not exist when using spiral designs, since the distance to the center changes continuously, so that the coils can be easily wound up. However, it might be worth the To provide cylindrical mounting elements with wedges or similar features to ensure correct bending of the coil elements in the construction of the gradient system.

Also according to the invention are those embodiments which are similar to a spiral or stepped construction. For example, it is possible for the conductor bridges 034a, 034b, or 035 to be steeper (even vertically) or flatter independently of each other; In this sense, the spiral design represents an extreme case of particularly flat conductor bridges. Also other than straight conductor bridges are conceivable, for example those with non-abrupt change of direction. A combination of helical and step-shaped construction could also be useful in individual cases.

The invention relates to such variations and other similar embodiments. It should be noted that the identical 120 ° symmetry relates only to the current-carrying conductors of the gradient system whose primary goal is to generate a magnetic field within the gradient system (the same applies to all gradient systems described in this document, including gradient systems with two identical transverse coils (see eg Fig. 7b or Fig. 7c ) or for the gradient systems according to the invention having a substantially planar or biplanar geometry). Auxiliary components such as gradient amplifiers are ignored, as are current-ingoing and outgoing conductors, unless they have a special geometry which serves to manipulate the gradient field generated and thus can be regarded as part of the gradient coil design itself. Thus, in the context of this invention, the symmetry property should be considered as obtained, for example, the power supply and discharge conductors are bundled for practicality reasons in one place to facilitate the connection with the gradient amplifiers, but without providing a significant contribution to the gradient field within the study area ,

z = [-60 cm, 60 cm]}. Die Wahl eines Designs mit einer azimutalen Ausdehnung von mehr als einer vollständigen Umrundung kann Vorteile bieten, insbesondere, wenn die Spulen kräftemäßig ausbalanciert sein sollen. Dies soll im Folgenden genauer erläutert werden.In the Fig. 3c shown gradient coils take differently than in Fig. 2 shown design an extension in the azimuthal direction of more than 360 °. Calculating such a design numerically does not present any difficulties, it is merely necessary to ensure that an angle Θ _max > 360 ° is selected during the parameterization of the surface, ie $S=\{\mathbf{x}\left(\mathrm{\theta },\mathrm{z}\right)\in {\mathbb{<figure-callout\; id="3"\; label="R"\; filenames="imgf0006.png"\; state="\{\{state\}\}">R</figure-callout>}}^3|\theta =\left[0°.{\Theta }_{\mathrm{Max}}\right].$

z = [-60 cm, 60 cm]}. The choice of a design with an azimuthal extension of more than one complete orbit may offer advantages, especially if the coils are to be balanced in terms of force. This will be explained in more detail below.

However, care is first taken, as is Fig. 4 results: Fig. 4 shows an open design with Θ _max > 360 °, which from the closed, in Fig. 1 shown balanced, balanced design was developed. Fig. 4a repeats the design in the black box Fig. 1 b. However, the current conductors 040 are cut at the two vertical black lines 041a and 041b . The open ends are then connected to each other via the gray drawn current conductors 042 and 043 . Since there are no large deviations, the following considerations can be ignored in a first approximation, the fact that such a design is difficult to realize on a pure cylinder surface, and should be better arranged spiral, stepped or similar, s. for example, the representation in Fig. 3c , Out Fig. 4a It will be seen that the additional current conductors 042 and 043 are exactly 360 ° apart or exactly one rotation. The effect of these additional currents is therefore the same as in Fig. 4b drawn in which the conductors 043 are shown offset by one rotation. Out Fig. 4b it now appears that the additional connecting conductors form current loops ("additional currents" = additional currents). These current loops are (almost) on a cylinder surface and thus have a magnetic moment in the radial direction. This magnetic moment interacts with the main magnetic field. Since the main magnetic field is aligned along the z-axis, results in a resulting torque in the azimuthal direction. This in Fig. 4a The design shown is therefore not balanced in terms of strength.

There are now several ways to deal with this problem. One possibility is to accept a design that is not 100% balanced in terms of strength.

For example, a meaningful design could be developed in such a way that the term λM in the objective function Φ is replaced by the term ωM , where ω is not a vector of three Lagrange multipliers, but a vector with three additional weights, by varying the degree can be adapted to how much the resulting design is balanced in terms of strength.

Another possibility is as in Fig. 4c shown to compensate the uncompensated currents by counter currents ("compensating currents" = compensating currents). This can be done by applying appropriate reverse voltages at the beginning and end of each in Fig. 4a gray drawn current conductors 042 and 043 done or through a separate compensation coil using its own gradient amplifier or the same, which is used for the main gradient coil.

At the in Fig. 4 shown arrangement of conductors offers an approximation of in Fig. 4c represented loop-shaped conductor 045 by a single vortex-shaped conductor. The compensation coil could also be realized by arranging the conductors 044a and 044b which connect the current-carrying conductors of the gradient coil to the current source so as to equalize the uncompensated torque.

There is also the possibility of a half-open design in which a part of the current conductors of one end are connected to the other end, but a part similar to the gray-colored conductors at the coil end recycled become. This increases efficiency, reduces the problem of balance of forces (ie, balance in terms of power), and simplifies wiring even in inventive, for example, spiral designs.

Furthermore, it can be very useful to develop a vigorously balanced basic design from the outset. That this is possible without major difficulties, shows Fig. 5 , Here are three situations, based on the closed, balanced and balanced design of Fig. 1 to show open designs. Only a single conductor loop is shown (irrelevant to the considerations is that the conductor loop is shown self-contained, similar to a contour line of the stream function; for a practical design, the conductor is slightly offset laterally after rounding, as in FIG Fig. 4 shown). For the problem of balance of forces, it is sufficient to consider a single conductor loop, the considerations can be easily generalized to several rounding. Fig. 5a shows a situation with positive torque, Fig. 5b with negative torque and Fig. 5c with no net torque.

Look first Fig. 5a , This situation corresponds directly to the one in Fig. 4 illustrated situation. The conductor loop shown consists of the balanced power conductors 050 and the connecting conductors 051a, 051b. Here, an angle Θ _{max was} chosen, which is significantly larger than 360 °; this angle also describes in this connection the expansion of the gradient coil in the azimuthal direction. As based on Fig. 4 already shown, this results in a positive (it is definitional matter whether a torque is called positive or negative, if the current flows in a clockwise direction, where the torque is defined as positive in the clockwise direction) net torque, which by the Main magnetic field acts on the gradient coil. An oppositely directed (negative) Torque arises in the in Fig. 5b illustrated situation. Here an angle of Θ _max = 360 ° was chosen.

As Fig. 2 Although it is also possible for this situation to design a force balanced design, a simple connection of the upper and lower conductors through the conductor sections 052a, 052b will result in a total negative torque. It has to be taken into account that the conductor pieces 053a - 053d used for the balanced, balanced design no longer have to be used, and thus de facto an opposing current in these conductor pieces must be taken into account in the calculation of the net current change. This results in a net loop in the form 054 with negative torque.

Thus, if too small an angle (Θ _max = 360 °) has a negative torque in this case, a positive torque exists if the angle is set too large. There must thus be an optimum angle at which the resulting torque disappears exactly.

This situation is in Fig. 5c shown. It can be seen that even in this situation Θ _{max is} greater than 360 °. The net current loop 057 in this case can obviously be decomposed into three smaller loops, two of which generate a negative torque and one a positive torque. At the point where the addition of the three torques results in zero, the result is a design that is balanced in terms of power.

The person skilled in the art knows how torques M can be calculated. So he knows that it results from the vector product of magnetic moment m and magnetic field B , ie M = m × B , where m = I / 2 ∫ _┌ x × dx; in this definition, I denotes the current in a conductor along the curve ┌ and x denotes the position vector.

For example, the resulting torque for a planar conductor loop is proportional to the area enclosed by the conductor loop, where the area counts positive with current flow in the positive direction and negative with current flow in the negative direction. Thus, in a first approximation, a balanced design is characterized by the fact that in the three-part net current loop 057, the sum of the upper and lower surfaces is just the average area.

This is true only approximately for cylindrical designs, since they are not planar conductor loops, but the skilled person knows how he would have to perform exact calculations; For example, he could use the formula given above to calculate the torque.

In summary, it can be said that it may well have technical advantages to choose an arrangement with an extension along the azimuthal direction of more than one rounding. In this case, a few degrees may be sufficient, however, the greater the extent of the gradient coil in the azimuthal direction, the more degrees of freedom and therefore optimization possibilities are available, since in this case a larger area is available for the placement of conductors.

Such a design can be realized by a helical, but also by a stepped or similar structure of the gradient system. In addition to fully open designs, partially open (ie semi-closed) designs may be used to increase efficiency, with only a portion of the live conductors such as the Fig. 4 or Fig. 5 is shown, the other part but forms closed conductors, as in Fig. 1 shown.

Fig. 6 indicates a problem that can occur when a closed design according to the invention is chosen, such as that in FIG Fig. 3b shown stepped design. If such a closed design is constructed, care must be taken that tracks can intersect.

This is in Fig. 6a Figure 11 illustrates a side view of a portion of a closed spiral design that has similar problems in this regard as for stepped designs. The arrows indicate the radial direction inwards (inwards) and outwards (outwards). After rounding, a coil reaches its maximum outside radius at 060. To connect the conductors to the other end of the coil, inside at 063 , the two other two coil layers must be crossed at 061 and 062.

This is technically quite feasible, however Fig. 6b shows that there is sufficient space along the z-direction, so that the connecting conductors are led inwards at different points starting at 063a-063e and ending at 060a - 060e . However, slight modifications to the optimized design may be necessary, such as Fig. 6b illustrated. Fig. 6b is intended to indicate that vertical conductors connecting the outer conductor to the inner portion of the coil cause the other two gradient coils to be passed at a particular position.

Since it is a 120 ° symmetry, it is sufficient in Fig. 6b showing a top view of the coil geometry in θ - z coordinates to represent a single coil design; the points at which the two other layers must be crossed are offset by 120 ° and 240 ° (= -120 °) and are designated 062a - 062e and 061a - 061e , respectively.

It is noticeable that there are areas where the density of the conductors is low. In these areas, the vertical current conductors can pass through almost unhindered (possibly slight shifting or bending of conductors is necessary). However, there are also areas of higher conductor density, which can not be crossed easily. At these points it is necessary to make technical arrangements.

This can be achieved either by reducing the number of vertically extending conductors at high density locations of conductors (a) or by (b) increasing the density of the horizontal conductors (crossed by the vertical connecting conductors). is reduced.

1. (i) Die in Fig. 6 dargestellte Situation weicht mit einem Verkippungswinkel von 45° gegenüber der Transversalebene vom Optimum ab, welches bei 35,26° liegt. Wird der Verkippungswinkel reduziert, erhöht sich der Transversalanteil der Spule und der Longitudinalanteil wird kleiner. Da aber nur der Longitudinalanteil Wicklungen um den Spulenkörper mit sich bringt, reduziert sich die Anzahl der Wicklungen, wenn ein kleinerer Verkippungswinkel gewählt wird, so dass weniger vertikal verlaufende Stromleiter benötigt werden.
2. (ii) Eine weitere Möglichkeit, die Anzahl der vertikal verlaufenden Stromleiter in dichten Bereichen zu reduzieren besteht darin, die Position zu verändern, an der die Stromleiter von außen nach innen geführt werden. Dies kann durch eine Verschiebung entlang der z-Richtung oder aber der θ-Richtung erfolgen. Entlang der z-Richtung besteht sogar die Möglichkeit, einen einzigen, mehrere oder sogar alle Stromleiter über den Rand von z = ±60cm hinauszuführen, um sie dann neben der Spule von außen nach innen zu führen; wird dies getan, können die Stromleiter dann wieder entlang der entgegengesetzten z-Richtung an die richtige Position zurückgeführt werden. Diese Herangehensweise hat den Vorteil, dass keine störenden Stromleiter der anderen beiden Gradientenspulen passiert werden müssen. Außerdem hat ein Leiter, der entlang der z-Achse verläuft, keinen Beitrag zum für die Kodierung relevanten B_z -Feld, so dass diese Leiterstücke auf die Kodierung selbst so gut wie keinen Einfluss haben.
   Neben der Möglichkeit, die Stromleiter jenseits des Randes der Spule vertikal hinabzuführen, bietet vor allem auch die Mitte bei z = 0 viel Raum für vertikal querende Stromleiter. Wie schon angesprochen kann es aber auch nützlich sein, Stromleiter nicht nur an anderen Positionen in z-Richtung vertikal hinabzuführen, sondern auch an anderen Stellen in θ-Richtung. Dies ist unproblematisch, weil es die erfindungsgemäßen Spulendesigns in der Regel zulassen, dass die Gradientenspule einen Gesamtwinkel von θ _max > 360° umschließt. Bei geschlossenen Designs ist es dem Grunde nach gleichgültig, bei welchem θ -Winkel das eine mit dem anderen Ende verbunden wird. Es kann daher einfach eine Stelle gewählt werden, bei der die Dichte der zu passierenden Stromleiter gering genug ist, um passiert zu werden.
3. (iii) Eine dritte Möglichkeit, die Anzahl der vertikal verlaufenden Stromleiter zu reduzieren, besteht darin, keine vollständig geschlossenen Anordnungen von Stromleitern zu wählen, sondern halb-geschlossene Anordnungen, bei denen ein Teil der stromführenden Leiter mit den rücklaufenden Leitern auf der anderen Seite der z-Achse verbunden werden, bis hin zu vollständig offenen Anordnungen, bei denen überhaupt kein vertikal verlaufender Leiter benötigt wird, da in diesem Fall alle Leiter mit den rücklaufenden Leitern verbunden werden, wie in Fig. 4 dargestellt.

To (a): There are several ways to reduce the number of vertical conductors.

1. (i) The in Fig. 6 illustrated situation deviates from the optimum with a tilt angle of 45 ° relative to the transverse plane, which is at 35.26 °. If the tilt angle is reduced, the transversal component of the coil increases and the longitudinal component becomes smaller. However, since only the longitudinal portion involves windings around the bobbin, the number of windings is reduced when a smaller tilt angle is selected so that less vertical current conductors are needed.
2. (ii) Another way to reduce the number of vertically extending conductors in dense areas is to change the position at which the conductors are routed from outside to inside. This can be done by a displacement along the z-direction or the θ- direction. Along the z-direction there is even the possibility to lead a single, several or even all current conductors beyond the edge of z = ± 60 cm , in order to then lead them from outside to inside beside the coil; When this is done, the conductors can then be returned to the correct position along the opposite z-direction. This approach has the advantage that no disturbing current conductors of the other two gradient coils must be passed. In addition, a conductor that runs along the z-axis, no contribution to the B _z field relevant for the coding, so that these conductor pieces have virtually no influence on the coding itself.
   In addition to the ability to vertically down the electrical conductors beyond the edge of the coil, especially the middle at z = 0 offers much space for vertically crossing conductors. As already mentioned, however, it may also be useful to lead current conductors vertically not only at other positions in the z-direction but also in other places in the θ- direction. This is not a problem, because the coil designs according to the invention generally permit the gradient coil to encompass a total angle of θ _max > 360 °. With closed designs, it basically does not matter at what angle the one is connected to the other end. It is therefore easy to choose a location where the density of the current conductors to be passed is low enough to be passed.
3. (iii) A third way to reduce the number of vertically extending conductors is to choose not completely closed arrays of conductors, but semi-closed arrangements in which a portion of the live conductors are connected to the return conductors on the other side Z axis can be connected to fully open arrangements in which no vertically extending conductor is needed, since in this case all conductors are connected to the returning conductors, as in Fig. 4 shown.

In addition to these methods of reducing the number of vertically extending conductors in regions of high conductor density of the gradient coils to be passed, further variants of those just described are conceivable. However, method (b) can be used (alternatively or in addition), according to which the density of the horizontally extending current conductors is reduced at locations where vertical current conductors (which connect the outer to the inner part of a coil) intersect. This can be achieved by having is deviated from the optimum geometry by moving conductors in the θ - z plane appropriately.

It is also possible within limits to reduce the conductor cross section, at least in the z or the θ direction. However, this is limited, as this locally higher resistances are installed, where possibly a sufficient cooling would have to be ensured. However, cooling could be additionally installed along the vertically extending conductor, so that a reduction of the conductor cross-section would be conceivable. Due to the other methods presented here, however, this will generally not be necessary in order to realize a closed gradient system according to the invention.

In the in Fig. 6 According to the embodiment of the invention shown, the current conductors, which connect the outer to the inner part of the individual gradient coils, run vertically. This is useful insofar as such a current conduction can be realized in a structurally simple manner, because here, for example, there would simply be vertical holes after joining the three gradient coils (or even two, for example, in an x, y, z gradient system according to the invention) to drill into the mounting material. In the resulting openings then conductor pieces could then be inserted, which could then be soldered externally or internally, welded or connected by a similar processing step with the still open ends of the respective gradient coil. However, this is only one of many realizations according to the invention. Instead of vertical abrupt junctions, it is also possible to use non-abrupt bends of conductors while avoiding two welds, or even non-vertical joints, for example, with the aim of providing better sites for traversing the individual horizontal layers.

Fig. 7 shows an example of an inventive implementation of a (substantially) cylindrical gradient system, which field gradient generated along the x, y and z axes. Unlike in Fig. 3 Here are only two of the three gradient coils in comparison to the prior art modified designed. The current conductors of the z-gradient coil (074, 078) are in the illustrated embodiments on a cylindrical surface outside; This is not mandatory, but because of the compared to transversal coils but higher efficiency of the longitudinal coil but this is usually advisable. The transverse coils, however, are configured identically, rotated only by 90 ° to each other.

It would be possible, the structure of the invention, the in Fig. 3b and Fig. 3c 3, it is shown to apply analogously to two coils, that is, to construct two layers which are spirally, stepwise or similarly intermeshed, open, half-closed or closed. However, in the case of transverse coils, the absence of windings around the bobbin basically allows an open configuration.

In addition, another embodiment is possible in Fig. 7b and Fig. 7c shown, in which the individual transverse coil is not composed of one element, but each of two elements.

This is going out Fig. 7a seen. There is one with the in the second section to the detailed description Fig. 1 described optimized design 070 for a transverse coil. It is noticeable that no contour lines (and no current conductors) intersect the two black drawn lines 071a, 071b . Since the lines run along the z-direction and thus each have constant azimuthal angles, which are rotated by exactly 180 ° to each other, the coil geometry along these lines can be separated in fact; at best, it is necessary to connect centers of the current-carrying vortices via (not shown) conductor bridges in a known manner (similar to FIG Fig. 1 b) , Therefore, a gradient system with coil geometries as in Fig. 7b and Fig. 7c be shown to be advantageous a gradient system in which a splitting of the coil geometry is not performed in two opposite parts.

Is concrete in Fig. 7b a step-shaped gradient system shown in side view, which consists of the two parts (072a, 072b) of an x-gradient coil 072 and from the two parts (073a, 073b) of the y-gradient coil 073. A penetration of the gradient coils does not take place, it is an open design. The reason for this is that for a transverse coil usually no windings are necessary around the bobbin (see previous section). Fig. 7c shows a spiral design with outer radius 075a and inner radius 075b (the difference depends on the thickness of the current-carrying conductors used and their insulation, thus usually a few millimeters to a few centimeters). The x-gradient coil 076 consists of two spirally outwardly extending elements 076a, 076b; rotated by 90 ° are respectively the corresponding elements 077A, 077B of the y-gradient coil 077. The two gradient coils 076 and 077 are thus identical and are transferred to geometrically with each other when the gradient about the longitudinal axis of the cylindrical arrangement (ie around the cylinder axis ) is rotated through an angle of 90 °, regardless of whether one or the other direction is rotated.

The arrangement thus has a 90 ° symmetry with respect to the two identical gradient coils, each transverse coil consisting of two elements each having an extension of 180 ° in the azimuthal direction and being rotated by 180 °, each element itself being open, helical ( Fig. 7c ) or stepped ( Fig. 7b ) is designed with a step in the middle between 0 ° and 180 °. Optionally, the coils may be equipped with possibly similarly stepped or spiral compensating coils, but contrarily constructed so that the radius does not grow in the same clockwise direction as that of the main coils (see above) Fig. 7b, Fig. 7c ), but in the opposite direction, analogous to that in the first section for a detailed description of Fig. 3 described situation. The advantages and disadvantages of stepped or spiral three-layer designs described in the above-mentioned section also apply correspondingly to the xyz gradient systems of the invention described herein. The same applies likewise to those in the first section for a detailed description of Fig. 3 discussed variations of such designs.

Fig. 8 shows the surface 080 of a single gradient coil for a planar gradient system (or of a lower or upper element of a gradient coil of a biplanar gradient system) from two perspectives, from above (FIG. Fig. 8a ) as well as from above ( Fig. 8b ).

The embodiment shown is circular, but other planar geometries are conceivable, such as squares or rectangles. From the prior art surfaces are known which lie in one plane. In order to construct a gradient system according to the invention with identical, only mutually rotated gradient coils, this planar geometry is cut at one point and one edge 082 is bent upwards relative to the other edge 083 . To make this possible, a small opening 081 is left in the middle, which is chosen as small as possible, but large enough not to damage the material to be bent. The resulting area of current-carrying conductors is only substantially planar after this process. However, in the context of this invention, a gradient system which is constructed from such substantially planar gradient coils is also referred to as planar (or biplanar). This linguistic simplification usually also applies to the gradient coils themselves, or to the surfaces formed by the arrangements of the current-carrying conductors (although these surfaces strictly speaking have a slight curvature). This linguistic simplification is also useful when talking about planar or curved surfaces.

Now it is possible to interleave two (for example, for x and y gradients) or three (for example for a magic angle gradient system) of such deformed gradient coils, so that they can be rotated by 90 ° (for x and y gradients). or by 120 ° (for the three Magic Angle gradient) are rotated against each other. Pictured is a geometry with exactly one rotation; analogous to the in Fig. 3c However, it is also possible to choose an angle of more than 360 ° so that parts of the respective gradient coil (or parts of a gradient coil element) overlap.

Also conceivable, analogously to the embodiments for cylindrical gradient systems according to the invention described in detail above, are open, half-closed and completely closed designs, wherein an approach can be chosen for the wiring as described above in the second section of the detailed description Fig. 6 described to ensure useful wiring. Also, care should generally be taken to ensure that the coils are balanced in terms of power and it can often be useful to complement the main coils with possibly geometrically similarly designed compensation coils.

REFERENCES Cited patent literature

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• [1] P. C. LAUTERBUR, Image formation by induced local interactions: Examples employing nuclear magnetic resonance, Nature, 242 (1973), pp. 190-191 .
• [2] P. MANSFIELD AND P. K. GRANNELL, NMR "diffraction" in solids?, J. Phys. C: Solid State Phys., 6 (1973), pp. L422-L426 .
• [3] M. HAACKE, R. W. BROWN, M. R. THOMPSON, AND R. VENKATESAN, Magnetic Resonance Imaging: Physical Principles and Sequence Design, Wiley, 1999 .
• [4] M. POOLE AND R. BOWTELL, Novel Gradient Coils Designed Using a Boundary Element Method, Concepts in Magn. Reson. Part B 31B (2007), pp. 162 -175 .
• [5] R. TURNER, A target field approach to optimal coil design, J. Phys. D: Appl. Phys. 19 (1986), pp. L147-L151 . doi:10.1088/0022-3727/19/8/001
• [6] R. TURNER, Gradient Coil Design: A Review of Methods, Magn. Reson. Imaging 11 (1993), pp. 903-920 .
• [7] R. A. LEMDIASOV AND R. LUDWIG, A Stream Function Method for Gradient Coil Desig, Concepts in Magn. Reson. Part B 26B (2005), pp. 67 - 80 .
• [8] G. N. PEEREN, Stream Function Approach for Determining Optimal Surface Currents, J. Comp. Phys. 191 (2003), pp. 305 - 321 .
• [9] R. WHILE, 3D Gradient Coil Design - Toroidal Surfaces, JMR 198(1) (2009), pp. 31-40 .
• [10] P. MANSFIELD AND B. CHAPMAN, Active Magnetic Screening of Coils for Static and Time-Dependent Magnetic Field Generation in NMR Imaging, J. Phys. E: Sci. Instrum. 19 (1986), pp. 540 - 545 .
• [11] R. BOWTELL AND P. MANSFIELD, Gradient Coil Design Using Active Magnetic Screening, Magn. Reson. Med. 17 (1991), pp. 15 - 21 .
• [12] S. SHVARTSMAN, M. MORICH, G. DEMEESTER AND Z. ZHAI, Ultrashort Shielded Gradient Coil Design with 3D Geometry, Concepts in Magn. Reson. Part B 26B (2005), pp. 1 - 15 .
• [13] M. S. POOLE, P. T. WHILE, H. S. LOPEZ AND S. CROZIER, Minimax Current Density Gradient Coils: Analysis of Coil Performance and Heating, Magn. Reson. Med. 68 (2012), pp. 639 - 648 .

The skilled artisan is advised to consult the scientific literature cited herein in order to best utilize the present invention. At selected points within the description, reference is explicitly made to the literature specified here.

• [1] PC LAUTERBUR, Image formation by induced local interactions: Examples of employing nuclear magnetic resonance, Nature, 242 (1973), pp. 190-191 ,
• [2] P. MANSFIELD AND PK GRANNELL, NMR "diffraction" in solids ?, J. Phys. C: Solid State Phys., 6 (1973), pp. L422-L426 ,
• [3] M. HAACKE, RW BROWN, MR THOMPSON, AND R. VENKATESAN, Magnetic Resonance Imaging: Physical Principles and Sequence Design, Wiley, 1999 ,
• [4] M. POOLE AND R. BOWTELL, Novel Gradient Coils Designed Using a Boundary Element Method, Concepts in Magn. Reson. Part B 31B (2007), pp. 162-175 ,
• [5] R. TURNER, A target field approach to optimal coil design, J. Phys. D: Appl. Phys. 19 (1986), pp. L147-L151 , doi: 10.1088 / 0022-3727 / 19/8/001
• [6] R. TURNER, Gradient Coil Design: A Review of Methods, Magn. Reson. Imaging 11 (1993), pp. 903-920 ,
• [7] RA LEMDIASOV AND R. LUDWIG, A Stream Function Method for Gradient Coil Desig, Concepts in Magn. Reson. Part B 26B (2005), pp. 67 - 80 ,
• [8th] GN PEEREN, Stream Function Approach for Determining Optimal Surface Currents, J. Comp. Phys. 191 (2003), pp. 305 - 321 ,
• [9] R. WHILE, 3D Gradient Coil Design - Toroidal Surfaces, JMR 198 (1) (2009), pp. 31-40 ,
• [10] P. MANSFIELD AND B. CHAPMAN, Active Magnetic Screening of Coils for Static and Time-Dependent Magnetic Field Generation in NMR Imaging, J. Phys. E: Sci. Instrum. 19 (1986), pp. 540 - 545 ,
• [11] R. BOWTELL AND P. MANSFIELD, Gradient Coil Design Using Active Magnetic Screening, Magn. Reson. Med. 17 (1991), pp. 15-21 ,
• [12] S. SHVARTSMAN, M. MORICH, G. DEMEESTER AND Z. ZHAI, Ultrashort Shielded Gradient Coil Design with 3D Geometry, Concepts in Magn. Reson. Part B 26B (2005), pp. 1 - 15 ,
• [13] MS POOLE, PT WHILE, HS LOPEZ AND S. CROZIER, Minimax Current Density Gradient Coils: Analysis of Coil Performance and Heating, Magn. Reson. Med. 68 (2012), pp. 639-648 ,

Claims (14)

A magnetic resonance imaging gradient system comprising three gradient coils (032) which a. current-carrying conductors (013) arranged on planar or curved surfaces (080, 030a), wherein the current-carrying conductors of n of the three gradient coils, with n = 2 or n = 3, are closed in the azimuthal direction, half-closed or open are formed (013, 021) and b. each generate a magnetic gradient field, wherein the gradient directions are orthogonal to each other, characterized,
in that the planar or curved surfaces (080, 030a) of the n gradient coils are formed spirally (036) and / or step-shaped (032),
and that the current-carrying conductors of the n gradient coils are identically shaped (038a, 038b, 038c). Gradient system according to claim 1, characterized in that the n identical gradient coils are converted into each other when the gradient system about a z-axis of the gradient system in the case of n = 2 by an angle α 1 = 90 ° or in the case of n = 3 by one Angle α 2 = 120 ° is rotated, regardless of whether rotated in one direction or the other, the gradient system thus with respect to the n identical gradient coils in the case of n = 2 a 90 ° symmetry (076, 077) or in the case of n = 3 has a 120 ° symmetry (038a, 038b, 038c). Gradient system according to claim 2, characterized in that the gradient system is cylindrical (020) and that the z-axis corresponds to the cylinder axis. Gradient system according to claim 3, characterized in that n = 3 and α 2 = 120 °, and that the extension of the n gradient coils in the azimuthal direction is 360 ° (032). Gradient system according to claim 3, characterized in that n = 3 and α 2 = 120 °, and that the extension of the n gradient coils in the azimuthal direction is more than 360 ° (038a, 038b, 038c). Gradient system according to claim 3, characterized in that n = 2 and α 1 = 90 °, and that the n = 2 identical gradient coils form transverse coils (072, 073) which generate orthogonal gradient fields in the transverse plane of the cylindrical geometry of the gradient system and the third Gradient coil is designed as a longitudinal coil (074), and wherein the two transverse coils are formed in the azimuthal direction open, half-closed or closed (072, 073). Gradient system according to claim 6, characterized in that each transverse coil consists of two elements which each have an extension of 180 ° in the azimuthal direction and are rotated by 180 ° to each other, each element itself a. open (072a, 072b), b. spiral (076a, 076b) or c. stepped with a step in the middle between 0 ° and 180 ° (072a, 072b) is designed. Gradient system according to claim 2, characterized in that the gradient system is formed planar or biplanar (080), and that the z-axis corresponds to that axis which is oriented orthogonal to the planar or biplanar conductor surfaces. Gradient system according to claim 8, characterized in that n = 3 and α 2 = 120 °. Gradient system according to claim 8, characterized in that n = 2 and α 1 = 90 °, and that the n = 2 identical gradient coils form transverse coils which generate orthogonal gradient fields in the transverse plane of the planar or bi-planar geometry of the gradient system, and the third gradient coil is designed as a longitudinal coil. Gradient system according to one of the preceding claims, characterized in that the three gradient coils are supplemented by compensation coils for an active shielding of the magnetic fields to the outside (033). Gradient system according to one of the preceding claims, characterized in that the three gradient coils are balanced in terms of their forces (057). A gradient coil for use in a gradient system according to any one of the preceding claims, wherein the gradient coil comprises current-carrying conductors (013) arranged on a planar or curved surface (080, 030a) and closed, half-closed or open-shaped in the azimuthal direction (013, 021) ), and wherein the gradient coil is constructed from one (038a) or from two elements (072a, 072b) and, if the gradient coil consists of one element, has an extension in the azimuthal direction of 360 ° (032) or more (038a, 038b, 038c) or, if the gradient coil consists of two elements, each element has an extension in the azimuthal direction of 180 ° (072a, 072b),
characterized,
that each element spiral (076a) and / or step-shaped (072A) is formed. Gradient coil according to claim 13, characterized in that in (n-1) -fold identical replica of the gradient coil, with n = 2 or n = 3, the surfaces on which the current-carrying conductors of the n gradient coils are arranged, do not penetrate.

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